We propose two positive parameters based on the choice of Birgin and Martínez search direction. Using classical choices Barzilai-Borwein parameters, were derived by minimizing distance between relative matrix corresponding to direction scaled memory-less Broyden–Fletcher–Goldfarb-Shanno (BFGS) in Frobenius norm. Moreover, resulting is descent independent any line condition. established global c...

We discuss the BFGS method on Riemannian manifolds and put a special focus on the degrees of freedom which are offered by this generalization. Furthermore, we give an analysis of the BFGS method on Riemannian manifolds that are isometric toRn.

Various model-based diagnosis scenarios require the computation of most preferred fault explanations. Existing algorithms that are sound (i.e., output only actual explanations) and complete can return all explanations), however, exponential space to achieve this task. As a remedy, we propose two novel diagnostic search algorithms, called RBF-HS (Recursive Best-First Hitting Set Search) HBF-HS (...

This chapter presents the Nelder–Mead simplex method and the Broyden– Fletcher–Goldfarb–Shanno (BFGS) method for finite-element-model updating. The methods presented have been tested on a simple beam and an unsymmetrical H-shaped structure. It was noted that, on average, the Nelder–Mead simplex method gives more accurate results than did the BFGS method. This is mainly because the BFGS method r...

A new method for designing IIR digital filters with linear phase in the passband is proposed. This method is based on frequency weighted least-square error optimization using the BFGS method [15]. The gradient of the cost function with respect to the design parameters, required for the implementation of the BFGS method, is derived. The proposed method is started by obtaining an initial IIR filt...

We present a three-dimensional (3-D) visualization of jet geometry using numerical methods based on Markov Chain Monte Carlo (MCMC) and limited memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimized algorithm. Our aim is to visualize the 3-D an active galactic nucleus (AGN) observations, which are inherently two-dimensional (2-D) images. Many AGN jets display complex structures that include h...

State-of-the-art methods for solving smooth optimization problems are nonlinear conjugate gradient, low memory BFGS, and Majorize-Minimize (MM) subspace algorithms. The MM subspace algorithm which has been introduced more recently has shown good practical performance when compared with other methods on various optimization problems arising in signal and image processing. However, to the best of...